Applying Formal Methods to Networking: Theory, Techniques and Applications

Despite its great importance, modern network infrastructure is remarkable for the lack of rigor in its engineering. The Internet which began as a research experiment was never designed to handle the users and applications it hosts today. The lack of formalization of the Internet architecture meant limited abstractions and modularity, especially for the control and management planes, thus requiring for every new need a new protocol built from scratch. This led to an unwieldy ossified Internet architecture resistant to any attempts at formal verification, and an Internet culture where expediency and pragmatism are favored over formal correctness. Fortunately, recent work in the space of clean slate Internet design---especially, the software defined networking (SDN) paradigm---offers the Internet community another chance to develop the right kind of architecture and abstractions. This has also led to a great resurgence in interest of applying formal methods to specification, verification, and synthesis of networking protocols and applications. In this paper, we present a self-contained tutorial of the formidable amount of work that has been done in formal methods, and present a survey of its applications to networking.Comment: 30 pages, submitted to IEEE Communications Surveys and Tutorial

On the Termination Problem for Probabilistic Higher-Order Recursive Programs

In the last two decades, there has been much progress on model checking of both probabilistic systems and higher-order programs. In spite of the emergence of higher-order probabilistic programming languages, not much has been done to combine those two approaches. In this paper, we initiate a study on the probabilistic higher-order model checking problem, by giving some first theoretical and experimental results. As a first step towards our goal, we introduce PHORS, a probabilistic extension of higher-order recursion schemes (HORS), as a model of probabilistic higher-order programs. The model of PHORS may alternatively be viewed as a higher-order extension of recursive Markov chains. We then investigate the probabilistic termination problem -- or, equivalently, the probabilistic reachability problem. We prove that almost sure termination of order-2 PHORS is undecidable. We also provide a fixpoint characterization of the termination probability of PHORS, and develop a sound (but possibly incomplete) procedure for approximately computing the termination probability. We have implemented the procedure for order-2 PHORSs, and confirmed that the procedure works well through preliminary experiments that are reported at the end of the article

Pruning, Pushdown Exception-Flow Analysis

Statically reasoning in the presence of exceptions and about the effects of exceptions is challenging: exception-flows are mutually determined by traditional control-flow and points-to analyses. We tackle the challenge of analyzing exception-flows from two angles. First, from the angle of pruning control-flows (both normal and exceptional), we derive a pushdown framework for an object-oriented language with full-featured exceptions. Unlike traditional analyses, it allows precise matching of throwers to catchers. Second, from the angle of pruning points-to information, we generalize abstract garbage collection to object-oriented programs and enhance it with liveness analysis. We then seamlessly weave the techniques into enhanced reachability computation, yielding highly precise exception-flow analysis, without becoming intractable, even for large applications. We evaluate our pruned, pushdown exception-flow analysis, comparing it with an established analysis on large scale standard Java benchmarks. The results show that our analysis significantly improves analysis precision over traditional analysis within a reasonable analysis time.Comment: 14th IEEE International Working Conference on Source Code Analysis and Manipulatio

Consistent SDNs through Network State Fuzzing

The conventional wisdom is that a software-defined network (SDN) operates under the premise that the logically centralized control plane has an accurate representation of the actual data plane state. Unfortunately, bugs, misconfigurations, faults or attacks can introduce inconsistencies that undermine correct operation. Previous work in this area, however, lacks a holistic methodology to tackle this problem and thus, addresses only certain parts of the problem. Yet, the consistency of the overall system is only as good as its least consistent part. Motivated by an analogy of network consistency checking with program testing, we propose to add active probe-based network state fuzzing to our consistency check repertoire. Hereby, our system, PAZZ, combines production traffic with active probes to periodically test if the actual forwarding path and decision elements (on the data plane) correspond to the expected ones (on the control plane). Our insight is that active traffic covers the inconsistency cases beyond the ones identified by passive traffic. PAZZ prototype was built and evaluated on topologies of varying scale and complexity. Our results show that PAZZ requires minimal network resources to detect persistent data plane faults through fuzzing and localize them quickly while outperforming baseline approaches.Comment: Added three extra relevant references, the arXiv later was accepted in IEEE Transactions of Network and Service Management (TNSM), 2019 with the title "Towards Consistent SDNs: A Case for Network State Fuzzing

Consistent SDNs through Network State Fuzzing

The conventional wisdom is that a software-defined network (SDN) operates under the premise that the logically centralized control plane has an accurate representation of the actual data plane state. Nevertheless, bugs, misconfigurations, faults or attacks can introduce inconsistencies that undermine correct operation. Previous work in this area, however, lacks a holistic methodology to tackle this problem and thus, addresses only certain parts of the problem. Yet, the consistency of the overall system is only as good as its least consistent part. Motivated by an analogy of network consistency checking with program testing, we propose to add active probe-based network state fuzzing to our consistency check repertoire. Hereby, our system, PAZZ, combines production traffic with active probes to continuously test if the actual forwarding path and decision elements (on the data plane) correspond to the expected ones (on the control plane). Our insight is that active traffic covers the inconsistency cases beyond the ones identified by passive traffic. PAZZ prototype was built and evaluated on topologies of varying scale and complexity. Our results show that PAZZ requires minimal network resources to detect persistent data plane faults through fuzzing and localize them quickly

Finite Countermodel Based Verification for Program Transformation (A Case Study)

Both automatic program verification and program transformation are based on program analysis. In the past decade a number of approaches using various automatic general-purpose program transformation techniques (partial deduction, specialization, supercompilation) for verification of unreachability properties of computing systems were introduced and demonstrated. On the other hand, the semantics based unfold-fold program transformation methods pose themselves diverse kinds of reachability tasks and try to solve them, aiming at improving the semantics tree of the program being transformed. That means some general-purpose verification methods may be used for strengthening program transformation techniques. This paper considers the question how finite countermodels for safety verification method might be used in Turchin's supercompilation method. We extract a number of supercompilation sub-algorithms trying to solve reachability problems and demonstrate use of an external countermodel finder for solving some of the problems.Comment: In Proceedings VPT 2015, arXiv:1512.0221

The Complexity of Model Checking Higher-Order Fixpoint Logic

Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of programs that are not expressible in the modal \lambda-calculus. This paper provides complexity results for its model checking problem. In particular we consider those fragments of HFL built by using only types of bounded order k and arity m. We establish k-fold exponential time completeness for model checking each such fragment. For the upper bound we use fixpoint elimination to obtain reachability games that are singly-exponential in the size of the formula and k-fold exponential in the size of the underlying transition system. These games can be solved in deterministic linear time. As a simple consequence, we obtain an exponential time upper bound on the expression complexity of each such fragment. The lower bound is established by a reduction from the word problem for alternating (k-1)-fold exponential space bounded Turing Machines. Since there are fixed machines of that type whose word problems are already hard with respect to k-fold exponential time, we obtain, as a corollary, k-fold exponential time completeness for the data complexity of our fragments of HFL, provided m exceeds 3. This also yields a hierarchy result in expressive power.Comment: 33 pages, 2 figures, to be published in Logical Methods in Computer Scienc